In set theory and related branches of mathematics, a collection F of subsets of a given set S is called a family of subsets of S, or a family of sets over S. More generally, a collection of any sets whatsoever is called a family of sets.
The term "collection" is used here because, in some contexts, a family of sets may be allowed to contain repeated copies of any given member, and in other contexts it may form a proper class rather than a set.
Read more about Family Of Sets: Examples, Properties, Hall's Marriage Theorem, Related Concepts
Famous quotes containing the words family of, family and/or sets:
“The same dreadful set,
the same family of orange and pink faces
carved and dressed up like puppets
who wait for their jaws to open and shut.”
—Anne Sexton (1928–1974)
“We have a great deal more kindness than is ever spoken. Maugre all the selfishness that chills like east winds the world, the whole human family is bathed with an element of love like a fine ether.”
—Ralph Waldo Emerson (1803–1882)
“The vain man does not wish so much to be prominent as to feel himself prominent; he therefore disdains none of the expedients for self-deception and self-outwitting. It is not the opinion of others that he sets his heart on, but his opinion of their opinion.”
—Friedrich Nietzsche (1844–1900)